TSTP Solution File: SET793+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET793+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:22:17 EDT 2022

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   65 (   5 unt;   0 def)
%            Number of atoms       :  219 (  11 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  241 (  87   ~;  92   |;  37   &)
%                                         (   9 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   5 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-3 aty)
%            Number of variables   :  115 ( 103   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f142,plain,
    $false,
    inference(avatar_sat_refutation,[],[f90,f96,f111,f127,f141]) ).

fof(f141,plain,
    ( ~ spl4_1
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(avatar_contradiction_clause,[],[f140]) ).

fof(f140,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(subsumption_resolution,[],[f139,f51]) ).

fof(f51,plain,
    ~ greatest(sK2,sK1,sK0),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ( ~ greatest(sK2,sK1,sK0)
    & total_order(sK1,sK0)
    & max(sK2,sK1,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f30,f39]) ).

fof(f39,plain,
    ( ? [X0,X1,X2] :
        ( ~ greatest(X2,X1,X0)
        & total_order(X1,X0)
        & max(X2,X1,X0) )
   => ( ~ greatest(sK2,sK1,sK0)
      & total_order(sK1,sK0)
      & max(sK2,sK1,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ? [X0,X1,X2] :
      ( ~ greatest(X2,X1,X0)
      & total_order(X1,X0)
      & max(X2,X1,X0) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ? [X0,X2,X1] :
      ( ~ greatest(X2,X1,X0)
      & total_order(X1,X0)
      & max(X2,X1,X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ~ ! [X0,X2,X1] :
        ( ( total_order(X1,X0)
          & max(X2,X1,X0) )
       => greatest(X2,X1,X0) ),
    inference(rectify,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X1,X0,X5] :
        ( ( max(X5,X0,X1)
          & total_order(X0,X1) )
       => greatest(X5,X0,X1) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X1,X0,X5] :
      ( ( max(X5,X0,X1)
        & total_order(X0,X1) )
     => greatest(X5,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV5) ).

fof(f139,plain,
    ( greatest(sK2,sK1,sK0)
    | ~ spl4_1
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(subsumption_resolution,[],[f138,f128]) ).

fof(f128,plain,
    ( apply(sK1,sK2,sK2)
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(backward_demodulation,[],[f89,f106]) ).

fof(f106,plain,
    ( sK3(sK2,sK1,sK0) = sK2
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f104]) ).

fof(f104,plain,
    ( spl4_3
  <=> sK3(sK2,sK1,sK0) = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f89,plain,
    ( apply(sK1,sK2,sK3(sK2,sK1,sK0))
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f87]) ).

fof(f87,plain,
    ( spl4_2
  <=> apply(sK1,sK2,sK3(sK2,sK1,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f138,plain,
    ( ~ apply(sK1,sK2,sK2)
    | greatest(sK2,sK1,sK0)
    | ~ spl4_1
    | ~ spl4_3 ),
    inference(subsumption_resolution,[],[f136,f84]) ).

fof(f84,plain,
    ( member(sK2,sK0)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f83]) ).

fof(f83,plain,
    ( spl4_1
  <=> member(sK2,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f136,plain,
    ( ~ member(sK2,sK0)
    | greatest(sK2,sK1,sK0)
    | ~ apply(sK1,sK2,sK2)
    | ~ spl4_3 ),
    inference(superposition,[],[f55,f106]) ).

fof(f55,plain,
    ! [X2,X0,X1] :
      ( ~ apply(X1,sK3(X0,X1,X2),X0)
      | ~ member(X0,X2)
      | greatest(X0,X1,X2) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X2)
      | greatest(X0,X1,X2)
      | ( ~ apply(X1,sK3(X0,X1,X2),X0)
        & member(sK3(X0,X1,X2),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f34,f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ apply(X1,X3,X0)
          & member(X3,X2) )
     => ( ~ apply(X1,sK3(X0,X1,X2),X0)
        & member(sK3(X0,X1,X2),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X2)
      | greatest(X0,X1,X2)
      | ? [X3] :
          ( ~ apply(X1,X3,X0)
          & member(X3,X2) ) ),
    inference(flattening,[],[f33]) ).

fof(f33,plain,
    ! [X1,X2,X0] :
      ( greatest(X0,X1,X2)
      | ~ member(X0,X2)
      | ? [X3] :
          ( ~ apply(X1,X3,X0)
          & member(X3,X2) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X1,X2,X0] :
      ( ( member(X0,X2)
        & ! [X3] :
            ( member(X3,X2)
           => apply(X1,X3,X0) ) )
     => greatest(X0,X1,X2) ),
    inference(unused_predicate_definition_removal,[],[f21]) ).

fof(f21,plain,
    ! [X1,X2,X0] :
      ( ( member(X0,X2)
        & ! [X3] :
            ( member(X3,X2)
           => apply(X1,X3,X0) ) )
    <=> greatest(X0,X1,X2) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X5,X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X1)
           => apply(X0,X2,X5) )
        & member(X5,X1) )
    <=> greatest(X5,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greatest) ).

fof(f127,plain,
    ( ~ spl4_1
    | spl4_4 ),
    inference(avatar_contradiction_clause,[],[f126]) ).

fof(f126,plain,
    ( $false
    | ~ spl4_1
    | spl4_4 ),
    inference(subsumption_resolution,[],[f125,f84]) ).

fof(f125,plain,
    ( ~ member(sK2,sK0)
    | spl4_4 ),
    inference(subsumption_resolution,[],[f123,f51]) ).

fof(f123,plain,
    ( greatest(sK2,sK1,sK0)
    | ~ member(sK2,sK0)
    | spl4_4 ),
    inference(resolution,[],[f110,f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( member(sK3(X0,X1,X2),X2)
      | greatest(X0,X1,X2)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f110,plain,
    ( ~ member(sK3(sK2,sK1,sK0),sK0)
    | spl4_4 ),
    inference(avatar_component_clause,[],[f108]) ).

fof(f108,plain,
    ( spl4_4
  <=> member(sK3(sK2,sK1,sK0),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f111,plain,
    ( spl4_3
    | ~ spl4_4
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f102,f87,f108,f104]) ).

fof(f102,plain,
    ( ~ member(sK3(sK2,sK1,sK0),sK0)
    | sK3(sK2,sK1,sK0) = sK2
    | ~ spl4_2 ),
    inference(resolution,[],[f89,f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ~ apply(sK1,sK2,X0)
      | sK2 = X0
      | ~ member(X0,sK0) ),
    inference(resolution,[],[f49,f53]) ).

fof(f53,plain,
    ! [X2,X3,X0,X1] :
      ( ~ max(X0,X2,X1)
      | ~ member(X3,X1)
      | ~ apply(X2,X0,X3)
      | X0 = X3 ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ~ max(X0,X2,X1)
      | ( ! [X3] :
            ( X0 = X3
            | ~ apply(X2,X0,X3)
            | ~ member(X3,X1) )
        & member(X0,X1) ) ),
    inference(rectify,[],[f32]) ).

fof(f32,plain,
    ! [X1,X0,X2] :
      ( ~ max(X1,X2,X0)
      | ( ! [X3] :
            ( X1 = X3
            | ~ apply(X2,X1,X3)
            | ~ member(X3,X0) )
        & member(X1,X0) ) ),
    inference(flattening,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( X1 = X3
            | ~ apply(X2,X1,X3)
            | ~ member(X3,X0) )
        & member(X1,X0) )
      | ~ max(X1,X2,X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( max(X1,X2,X0)
     => ( ! [X3] :
            ( ( apply(X2,X1,X3)
              & member(X3,X0) )
           => X1 = X3 )
        & member(X1,X0) ) ),
    inference(unused_predicate_definition_removal,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( apply(X2,X1,X3)
              & member(X3,X0) )
           => X1 = X3 )
        & member(X1,X0) )
    <=> max(X1,X2,X0) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X5,X0] :
      ( ( ! [X2] :
            ( ( apply(X0,X5,X2)
              & member(X2,X1) )
           => X2 = X5 )
        & member(X5,X1) )
    <=> max(X5,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max) ).

fof(f49,plain,
    max(sK2,sK1,sK0),
    inference(cnf_transformation,[],[f40]) ).

fof(f96,plain,
    spl4_1,
    inference(avatar_contradiction_clause,[],[f95]) ).

fof(f95,plain,
    ( $false
    | spl4_1 ),
    inference(resolution,[],[f91,f49]) ).

fof(f91,plain,
    ( ! [X0] : ~ max(sK2,X0,sK0)
    | spl4_1 ),
    inference(resolution,[],[f85,f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( member(X0,X1)
      | ~ max(X0,X2,X1) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f85,plain,
    ( ~ member(sK2,sK0)
    | spl4_1 ),
    inference(avatar_component_clause,[],[f83]) ).

fof(f90,plain,
    ( ~ spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f81,f87,f83]) ).

fof(f81,plain,
    ( apply(sK1,sK2,sK3(sK2,sK1,sK0))
    | ~ member(sK2,sK0) ),
    inference(resolution,[],[f80,f51]) ).

fof(f80,plain,
    ! [X0] :
      ( greatest(X0,sK1,sK0)
      | ~ member(X0,sK0)
      | apply(sK1,X0,sK3(X0,sK1,sK0)) ),
    inference(duplicate_literal_removal,[],[f78]) ).

fof(f78,plain,
    ! [X0] :
      ( ~ member(X0,sK0)
      | apply(sK1,X0,sK3(X0,sK1,sK0))
      | greatest(X0,sK1,sK0)
      | ~ member(X0,sK0)
      | ~ member(X0,sK0)
      | greatest(X0,sK1,sK0) ),
    inference(resolution,[],[f65,f55]) ).

fof(f65,plain,
    ! [X3,X4,X5] :
      ( apply(sK1,sK3(X3,X4,sK0),X5)
      | ~ member(X3,sK0)
      | apply(sK1,X5,sK3(X3,X4,sK0))
      | greatest(X3,X4,sK0)
      | ~ member(X5,sK0) ),
    inference(resolution,[],[f57,f54]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ member(X0,sK0)
      | apply(sK1,X0,X1)
      | ~ member(X1,sK0)
      | apply(sK1,X1,X0) ),
    inference(resolution,[],[f50,f44]) ).

fof(f44,plain,
    ! [X2,X3,X0,X1] :
      ( ~ total_order(X1,X0)
      | apply(X1,X3,X2)
      | ~ member(X2,X0)
      | ~ member(X3,X0)
      | apply(X1,X2,X3) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ total_order(X1,X0)
      | ( order(X1,X0)
        & ! [X2,X3] :
            ( apply(X1,X3,X2)
            | apply(X1,X2,X3)
            | ~ member(X3,X0)
            | ~ member(X2,X0) ) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ( ~ total_order(X0,X1)
      | ( order(X0,X1)
        & ! [X3,X2] :
            ( apply(X0,X2,X3)
            | apply(X0,X3,X2)
            | ~ member(X2,X1)
            | ~ member(X3,X1) ) ) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( order(X0,X1)
        & ! [X3,X2] :
            ( apply(X0,X2,X3)
            | apply(X0,X3,X2)
            | ~ member(X3,X1)
            | ~ member(X2,X1) ) )
      | ~ total_order(X0,X1) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( total_order(X0,X1)
     => ( order(X0,X1)
        & ! [X3,X2] :
            ( ( member(X3,X1)
              & member(X2,X1) )
           => ( apply(X0,X2,X3)
              | apply(X0,X3,X2) ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ( order(X0,X1)
        & ! [X3,X2] :
            ( ( member(X3,X1)
              & member(X2,X1) )
           => ( apply(X0,X2,X3)
              | apply(X0,X3,X2) ) ) )
    <=> total_order(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_order) ).

fof(f50,plain,
    total_order(sK1,sK0),
    inference(cnf_transformation,[],[f40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET793+4 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 14:31:51 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.51  % (24077)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.52  % (24077)First to succeed.
% 0.21/0.52  % (24069)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.21/0.52  % (24086)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.53  % (24068)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.53  % (24067)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.53  % (24087)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.21/0.53  % (24077)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (24077)------------------------------
% 0.21/0.53  % (24077)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (24077)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (24077)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (24077)Memory used [KB]: 6140
% 0.21/0.53  % (24077)Time elapsed: 0.117 s
% 0.21/0.53  % (24077)Instructions burned: 6 (million)
% 0.21/0.53  % (24077)------------------------------
% 0.21/0.53  % (24077)------------------------------
% 0.21/0.53  % (24060)Success in time 0.173 s
%------------------------------------------------------------------------------